Suppose the time to process a loan application follows a uniform distribution over the range of 8 to 13 days. what is the probability that a randomly selected loan application takes longer than 12 days to process?

0.2

Step-by-step explanation:

We know that , the probability density function for uniform distribution is given buy :-

, where x is uniformly distributed in interval [a,b].

Given : The time to process a loan application follows a uniform distribution over the range of 8 to 13 days.

Let x denotes the time to process a loan application.

So the probability distribution function of x for interval[8,13] will be :-

Now , the probability that a randomly selected loan application takes longer than 12 days to process will be :-

Hence, the probability that a randomly selected loan application takes longer than 12 days to process = 0.2

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

are ya tryin to ask something or is this a statement